Data Entry: Program performs 1 analysis only   - The data is a table with 3 columns   - Each row is data related to the row value   - Column 1 is the x value for that row (x)   - Column 2 is the number with positive attributes in that row (N Pos)   - Column 3 is the number with negative attribute in that row (N Neg)

R Program for regression of proportion is a single conginuous program. To make it easier to follow, the listing is divided into 2 sections

Section 1: Initial data input and matrix of summaries

#   Section 1: Preparation
dat = ("
   X NPos  NNeg  
1990   10   100
1992    8    50
1995   61   300
       ")
df <- read.table(textConnection(dat),header=TRUE)  # conversion to data frame    
df$RowTot <- df$NPos + df$NNeg  # total number each row
df$Prob <- df$NPos / df$RowTot   # probability of Pos each row
df   # Summary of Input Data

The initial matrix with all the data necessary for calculations are as follows. Please note:

• X is the predictor in the regression formular, and should be at least ordinal and preferably intrval mesurements. In this example it represents the year the data is collected
• NPos is the number of cases with positive attributes
• NNeg is the number of cases with negative attributes
• RowTot is NPos + NNeg for the row
• Prob is probability, NPos / RowTot

> df   # Summary of Input Data
     X NPos NNeg RowTot       Prob
1 1990   10  100    110 0.09090909
2 1992    8   50     58 0.13793103
3 1995   61  300    361 0.16897507

Section 2 is the actual calculations

#  Preparation for calculation
rows = nrow(df)
posTot = sum(df$NPos)
negTot = sum(df$NNeg)
tot = sum(df$RowTot)

# vevtors for results
Source <- vector()
ChiSq <- vector()
DF <- vector()
P<- vector()

# calculate total chi sq
zw = 0
chiTot = 0
dfTot = rows - 1
for(i in 1:rows)                     # for each row
{
  zw = zw + df$X[i] * df$RowTot[i]   # row value x row count
  e = df$RowTot[i] * posTot / tot;   # expected
  o = df$NPos[i]                          # observed number pos
  chiTot = chiTot + (o - e)**2 / e        # add to Chi Sq
  e = df$RowTot[i] * negTot / tot;   # expected
  o = df$NNeg[i]                          # observed number beg
  chiTot = chiTot + (o - e)**2 / e        # add to Chi Sq
}
pTot = 1 - pchisq(chiTot, df=dfTot)  
Source <- append(Source, "Total")    # add to vectors for eventual display
ChiSq <- append(ChiSq, chiTot)
DF <- append(DF, dfTot)
P<- append(P,pTot)
#c(chiTot,pTot)

# Calculate regression and its chi sq
p2 = posTot / tot;         # probability of col 1
top = 0;
bot = 0;
for(i in 1:rows)
{
  top = top + df$X[i] * df$NPos[i]     # sum row value x col 1
  bot = bot + df$X[i]^2 * df$RowTot[i] # row val sq x row count
}
#Calculation of regression coefficient
top = top - posTot * zw / tot
bot = bot - zw^2 / tot
reg = top / bot      # regression coefficient
# calculate chi sq regression
chiReg = top^2 / (bot * p2 * (1 - p2))  # chi sq regression
pReg = 1 - pchisq(chiReg, df=1)
Source <- append(Source, "Regression")    # add to vectors for eventual display
ChiSq <- append(ChiSq, chiReg)
DF <- append(DF, 1)
P<- append(P,pReg)

# Calculate residual chi sq
chiRes = chiTot - chiReg        # chi sq residual
dfRes = dfTot - 1
pRes = 1 - pchisq(chiRes, df=dfRes)
Source <- append(Source, "Residual")    # add to vectors for eventual display
ChiSq <- append(ChiSq, chiRes)
DF <- append(DF, dfRes)
P<- append(P,pRes)

# output
dfRes <- data.frame(Source, ChiSq, DF, P)  # combine vectors into data frame for display
dfRes # display chi sq, df, and significance in p
# Regression coefficient
reg #regression coefficient changes in propbabilit per unit of X

The results are as follows

> dfRes
      Source      ChiSq DF          P
1      Total 4.11131566  2 0.12800860
2 Regression 4.01760141  1 0.04502771
3   Residual 0.09371425  1 0.75950732

> reg #regression coefficient changes in propbability per unit of X
[1] 0.014958